Hückel's rule

In organic chemistry, Hückel's rule estimates whether a planar ring molecule will have aromatic properties. The quantum mechanical basis for its formulation was first worked out by physical chemist Erich Hückel in 1931. The succinct expression as the 4n + 2 rule has been attributed to W. v. E. Doering (1951), although several authors were using this form at around the same time. In organic chemistry, Hückel's rule estimates whether a planar ring molecule will have aromatic properties. The quantum mechanical basis for its formulation was first worked out by physical chemist Erich Hückel in 1931. The succinct expression as the 4n + 2 rule has been attributed to W. v. E. Doering (1951), although several authors were using this form at around the same time. In keeping with the Möbius-Hückel concept, a cyclic ring molecule follows Hückel's rule when the number of its π-electrons equals 4n + 2 where n is a non-negative integer, although clearcut examples are really only established for values of n = 0 up to about n = 6. Hückel's rule was originally based on calculations using the Hückel method, although it can also be justified by considering a particle in a ring system, by the LCAO method and by the Pariser–Parr–Pople method. Aromatic compounds are more stable than theoretically predicted using hydrogenation data of simple alkenes; the additional stability is due to the delocalized cloud of electrons, called resonance energy. Criteria for simple aromatics are: The rule can be used to understand the stability of completely conjugated monocyclic hydrocarbons (known as annulenes) as well as their cations and anions.The best-known example is benzene (C6H6) with a conjugated system of six π electrons, which equals 4n + 2 for n = 1. The molecule undergoes substitution reactions which preserve the six π electron system rather than addition reactions which would destroy it. The stability of this π electron system is referred to as aromaticity. Still, in most cases, catalysts are necessary for substitution reactions to occur. The cyclopentadienyl anion (C5H–5) with six π electrons and is planar and readily generated from the unusually acidic cyclopentadiene (pKa 16), while the corresponding cation with four π electrons is destabilized, being harder to generate than a typical acyclic pentadienyl cations and is thought to be antiaromatic. Similarly, the tropylium cation (C7H+7), also with six π electrons, is so stable compared to a typical carbocation that its salts can be crystallized from ethanol. On the other hand, in contrast to cyclopentadiene, cycloheptatriene is not particularly acidic (pKa 37) and the anion is considered nonaromatic. The cyclopropenyl cation (C3H+3) and the triboracyclopropenyl dianion (B3H2–3) are considered examples of a two π electron system, which are stabilized relative to the open system, despite the angle strain imposed by the 60° bond angles. Planar ring molecules with 4n π electrons do not obey Hückel's rule, and theory predicts that they are less stable and have triplet ground states with two unpaired electrons. In practice such molecules distort from planar regular polygons. Cyclobutadiene (C4H4) with four π electrons is stable only at temperatures below 35 K and is rectangular rather than square. Cyclooctatetraene (C8H8) with eight π electrons has a nonplanar 'tub' structure. However the dianion C8H2–8 (cyclooctatetraenide anion), with ten π electrons obeys the 4n + 2 rule for n = 2 and is planar, while the 1,4-dimethyl derivative of the dication, with six π electrons, is also believed to be planar and aromatic. Cyclononatetraenide anion (C9H–9) is largest all-cis monocyclic annulene/annulenyl system that is planar and aromatic. These bond angles (140°) differ significantly from the ideal angles of 120°. Larger rings possess trans bonds to avoid the increased angle strain. However, 10 to 14-membered systems all experience considerable transannular strain. Thus, these systems are either nonaromatic or experience modest aromaticity. This changes when we get to annulene, with (4×4) + 2 = 18 π electrons, which is large enough to accommodate 6 interior hydrogens in a planar configuration (3 cis double bonds and 6 trans double bonds). Thermodynamic stabilization, NMR chemical shifts, and nearly equal bond lengths all point to considerable aromaticity for annulene. Hückel's rule is not valid for many compounds containing more than three fused aromatic nuclei in a cyclic fashion. For example, pyrene contains 16 conjugated electrons (8 bonds), and coronene contains 24 conjugated electrons (12 bonds). Both of these polycyclic molecules are aromatic, even though they fail the 4n + 2 rule. Indeed, Hückel's rule can only be theoretically justified for monocyclic systems. In 2000, Andreas Hirsch and coworkers in Erlangen, Germany, formulated a rule to determine when a fullerene would be aromatic. They found that if there were 2(n + 1)2 π-electrons, then the fullerene would display aromatic properties. This follows from the fact that an aromatic fullerene must have full icosahedral (or other appropriate) symmetry, so the molecular orbitals must be entirely filled. This is possible only if there are exactly 2(n + 1)2 electrons, where n is a nonnegative integer. In particular, for example, buckminsterfullerene, with 60 π-electrons, is non-aromatic, since 60 ÷ 2 = 30, which is not a perfect square. In 2011, Jordi Poater and Miquel Solà, expanded the rule to determine when a fullerene species would be aromatic. They found that if there were 2n2 + 2n + 1 π-electrons, then the fullerene would display aromatic properties. This follows from the fact that an spherical species having a same-spin half-filled last energy level with the whole inner levels being fully filled is also aromatic.